Complexity of the p-spin Hamiltonian with a Non-Rotationally Invariant Potential
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Chen, Wei-Kuo Lu, Te-Lun Sen, Arnab |
| author_facet | Chen, Wei-Kuo Lu, Te-Lun Sen, Arnab |
| contents | We investigate the complexity of the Hamiltonian in the pure $p$-spin spin glass model accompanied with a polynomial-type potential on $\mathbb{R}^N$. In this Hamiltonian, the Gaussian field is anisotropic, and the potential lacks rotational invariance. Our main result derives the logarithmic limit for the expected number of critical points in terms of a variational formula. As a consequence, by identifying the critical location of the phase transition from our representation, we provide an upper bound for the ground state energy of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complexity of the p-spin Hamiltonian with a Non-Rotationally Invariant Potential Chen, Wei-Kuo Lu, Te-Lun Sen, Arnab Probability 15A52, 82D30, 60G60, 60F10 We investigate the complexity of the Hamiltonian in the pure $p$-spin spin glass model accompanied with a polynomial-type potential on $\mathbb{R}^N$. In this Hamiltonian, the Gaussian field is anisotropic, and the potential lacks rotational invariance. Our main result derives the logarithmic limit for the expected number of critical points in terms of a variational formula. As a consequence, by identifying the critical location of the phase transition from our representation, we provide an upper bound for the ground state energy of the model. |
| title | Complexity of the p-spin Hamiltonian with a Non-Rotationally Invariant Potential |
| topic | Probability 15A52, 82D30, 60G60, 60F10 |
| url | https://arxiv.org/abs/2602.11036 |